The basic functionality of FL-L(S25FL064L belongs to FL-L family of devices) is supported by the Linux SPI driver you pointed. You might need to add the corresponding device ID entries to the code. Here is the list:

{ "s25fl064l", INFO(0x016017, 0, 64 * 1024, 128, SECT_4K) },

{ "s25fl128l", INFO(0x016018, 0, 64 * 1024, 256, SECT_4K) },

{ "s25fl256l", INFO(0x016019, 0, 64 * 1024, 512, SECT_4K) },

The SECT_4K flag can be omitted, if you want to use small 4k sectors or not. For a file system it is better to use larger sectors.